Saturday's confrontation signals "a different level of self confidence in Tehran and Damascus in terms of them having the upper hand in Syria," said Ofer Zalzberg, a Jerusalem-based senior analyst with the International Crisis Group.

He said Iran, Israel and Syria would likely continue to test each other's boundaries as each tries to “define the new rules of the game.”

The back-and-forth attacks demonstrate how the conflict in Syria — what began as a civil war nearly seven years ago — has turned into a broader power contest with ramifications for the entire region.

The showdown began with Israel shooting down an Iranian reconnaissance drone that Israel claimed had entered its airspace. Israel retaliated for the incursion by striking the Iranian base in Syria from which the drone was operated. A Syrian anti-aircraft missile hit one of the attacking Israeli F-16 jets, which crashed on Israeli soil after the two pilots ejected; both survived, but one was seriously injured.

By downing Iran’s drone and attacking its sites in Syria, Israel signaled that it has little tolerance for a stronger Iranian presence on its northern border.

An Israeli F-16 that crashed after coming under fire from Syrian air defenses on Saturday.Jack Guez / AFP - Getty Images

“Israel believes that it has to establish deterrence,” said Meir Javedanfar, a professor of Iranian politics at the Interdisciplinary Center in Herzliya, Israel. If Iran acts aggressively, Israel’s response will be “three or four times as severe to deter Iran from taking similar actions.”

On Tuesday, Syria's Assistant Foreign Minister Ayman Sussan warned Israel of "more surprises" if its forces make further incursions into Syrian territory.

The clashes with Iran have coincided with one of the roughest weeks in Israeli Prime Minister Benjamin Netanyahu’s political life. Israeli police recommended Tuesday that he should be indicted on charges of corruption and bribery. Netanyahu has denied all the charges and has vowed that he will be vindicated, but domestic pressure on the hawkish leader who has dominated Israeli politics for the last two decades is mounting.

“Two vectors are colliding”

Amos Yadlin, a retired major general in the Israeli air force and a former head of intelligence with the Israel Defense Forces, described last weekend's fighting as "very significant."

"There is a determination by Iran to build a military force in Syria and Lebanon, and there is determination in Israel not to let this happen," he said. "And the two vectors are colliding."

Yadlin suggested that Israel's actions were also intended to send a "strong diplomatic message" to the U.S. and Russia.

"Russia is not our enemy, but Russia has different interests than we have," he said. "I think that instead of pointing fingers we have to try and let the Russians understand that if they will support Iran and Hezbollah there will be an escalation and an escalation is not a Russian interest."

Yadlin added, "The strategic collision between the Iranian determination to build a force and the Israeli determination not to let them build the force in Syria and Lebanon is a potential for a war."

Paul Goldman contributed reporting from Tel Aviv.

CORRECTION (Feb. 17, 2018, 8:00 a.m. ET): An earlier version of this article misstated the timing of the Israeli pilots’ ejection from their jet. They ejected before their F-16 crashed, not afterwards.